Moduli Spaces of Curves: Classical and Tropical
Melody Chan · Notices of the American Mathematical Society · 2021
First, we give an informal and elementary introduction to the idea of a moduli space, and then to moduli spaces of Riemann surfaces and their Deligne-Mumford-Knudsen compactifications. Second, we discuss some tropical geometry, assuming no prior knowledge of the subject, and build up to some recent results on moduli spaces that were obtained using tropical techniques.